- Email: [email protected]
Heat of transport and heat of solution
Scripta M E T A L L U R G I C A
Vol. 13, pp. 631-634, 1979 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved.
HEAT OF T R A N S P O R T AND HEAT OF SOLUTION
J. Mathuni,
R. Kirchheim,
and E. Fromm
M a x - P l a n c k - I n s t i t u t ffir M e t a l l f o r s c h u n g Institut ffir W e r k s t o f f w i s s e n s c h a f t e n Stuttgart, Germany (Received May 2, 1979)
Introduction In the i n t e r p r e t a t i o n of the heat of transport, Q+, obtained from steady state c o n c e n t r a t i o n profiles, the partial molal enthalpy, h, or heat of solution of the m i g r a t i n g particles has sometimes been considered to be one part of this q u a n t i t y (I-3). This point is of particular interest for the transport of interstitial atoms d i s s o l v e d in metals, e.g. H,C,N or O, since their partial molal enthalpy values, h, are r e l a t i v e l y large and frequently much higher than the heat of transport. In the O- and N-systems of V, Nb or Ta this difference exceeds in some cases one order of m a g n i t u d e (1,3,4). Thus the experimental heat of transport value should contain, in addition to h, other contributions with opposite signs but of similar magnitude, e.g. 400 kJ/mol or more. This rather u n r e a s o n a b l e consequence as well as the fact that h depends on the definition of the standard state are plausible arguments against this kind of subdivision of Q+ into components. In this paper the basic equations of entropy p r o d u c t i o n and the flux equations are analysed again under this aspect and it is d e m o n s t r a t e d by appropriate definitions and transformations, that neither h itself nor its temperature dependence are a priori contained in components of Q+ d e t e r m i n e d in an experiment. Basic Equations For one sort of mobile particles i the entropy production in a volume element that is passed by the energy flux Ju and the particle flux Ji is given by (5) (I)
~=
Ju~I/T - Ji?~T .
W i t h ) / = h - Ts = h - Ts O - TR in (~'c), c mole fraction of i and ~ a c t i v i t y effidient this equation can be t r a n s f o r m e d to
(2)
~=
Ju" V l / T
(3)
= Ju" ~ I / T
- Ji
- Ji
or with
T %ln c T
-1--
1 9 h
(4)
~ I/T c
T ~I/T
= _ _ 9S
= - CpT
~I/T
+ R
and
1+ ~ l n ~ ? I n ~in c
m =91n
91/T
631 0036-9748/79/070631-04502.00/0 Copyright (c) 1979 Pergamon Press Ltd.
91n
~ I c T
c
co-
632
HEAT OF TRANSPORT AND HEAT 0F SOLUTION
(5)
~=
Vol.
13, No. 7
(Ju-Ji'h) ~ I/T - Ji-R. (1+m) V in c
Eq. (5) and the subsequent considerations are simplified by the introduction of the following definition for the energy flux: (6)
Ju = Jq + Ji h + Ji Q+
is the heat flux due to thermal conductivity in a temperature gradient and ~ shall contain no components coupled with the particle flux J~. The energy transferred together with the particles i under the condition o~ thermal equilibrium with their surrounding is Ji-h and Q+ is the energy transferred with the particles in excess of this equilibrium value as a consequence of the specific transport mechanism present. With Eq. (5) and (6) one obtains (7)
~=
Jq V I / T
If V I/T and the expression equations are
(8) (9)
Ji = L11 {Q+~I/T
+ Ji { Q + V I / T
- R(1+m) ~ in c ~
in brackets are choosen as driving
- R(1+m)Vlncl+
Jq = L21 {Q+~I/T
L12 ~ I / T
- R(1+m)~incj
= L11 ~Q+~I/T
+ L22~1/T
forces the flux
- R(1+m)~ I n c }
= L22~1/T
From the definition of Ja in Eq. (6) and Onsagers theorem it follows that the phenomenological coefficfents L21 and L12 are zero for this specific choice of fluxes and forces. The condition Ji = O for steady state yields immediately the well known expression (10)
Q+
R(1+m) =
dln c d I/T
and for ideal systems with m = O (11)
Q+
R d in c =
I/-----T d
Thus, the physical significance of the reduced heat of transport, in steady state experiments is exactly the same as in Eq. (6). In the standard treatment with (Ju-h.J i) as transformed energy flux, nomenological coefficients L11 and L22 no longer play any role in tion of Q+ and it is not necessary to distinguish between the two transport, Q~, and reduced heat of transport, Q+ = Q~-h.
Q+, measured contrast to the two phethe definiterms heat of
In steady s t a t e , b e c o m e s a minimum and in Eq. (7) the expression in brackets is zero. Q+- Vl/T represents the entropy change due to the fact that Q+ enters and leaves a volume element together with the particles at interfaces with different temperature and R(l+m) V l n c is the entropy change due to differences in the entropy of position. In steady state both components cancel and if a particle flux Ji would pass a volume element under these conditions it could not contribute to the entropy production. Conclusions Further definitions
and conclusions
derived from the equations used are:
Vol.
13, No.
7
HEAT OF T R A N S P O R T AND HEAT OF SOLUTION
633
a) The e x p r e s s i o n (Ju-Jih) in Eq. (5) states that the heat of s o l u t i o n transferred t o g e t h e r w i t h the i atoms is a c o m p o n e n t of the total e n e r g y flux Ju w h i c h does not change the e n t r o p y p r o d u c t i o n ~ . O n l y that part of the energy w h i c h is t r a n s f e r r e d w i t h m i g r a t i n g p a r t i c l e s in excess to the e q u i l i b r i u m energy h at the t e m p e r a t u r e c o n s i d e r e d can affect the e n t r o p y production. This d i f f e r e n c e in the energy flux term a u t o m a t i c a l l y solves the p r o b l e m of the a r b i t r a r y d e f i n i t i o n of the s t a n d a r d state of h and c o n s e q u e n t l y also of the total energy flux Ju" b) The t e m p e r a t u r e d e p e n d e n c e of h and s cancel in Eq. (3) and thus they are not able to i n f l u e n c e Q+. c) The a t o m i s t i c m o d e l s p r e s e n t l y d i s c u s s e d are c o n s i s t e n t w i t h the interpret a t i o n of Q+ used in Eq. (6). In W i r t z - t y p e models (6-10) Q+ is the activation energy or part of it. A jumping atoms gathers this energy from its surr o u n d i n g in the starting p o s i t i o n and releases it again to the lattice as heat e n e r g y after the jump. In e l e c t r o n drag theories (11-14) it is the difference in the energy t r a n s f e r b e t w e e n jumping p a r t i c l e s in the saddle point and e l e c t r o n and/or hole currents flowing p a r a l l e l and antiparallel, respectively, to the t e m p e r a t u r e gradient. ~+ (Ju-Jih) ; . d) The d e f i n i t i o n U = ~ ~T an~ further c o n c l u s i o n s d e r i v e d from this e x p r e s s i o n by Oriani (15) are in a g r e e m e n t w i t h the present i n t e r p r e t a t i o n of Q+. e) If t r a n s p o r t p h e n o m e n a are d i s c u s s e d in systems w h e r e the e x c h a n g e of particles w i t h the s u r r o u n d i n g gas a t m o s p h e r e occurs, the heat of solution, h, has to be c o n s i d e r e d in the t h e o r e t i c a l treatment, as it has been done, e.g., by H. Rickert and C. W a g n e r (16) because this energy is really t r a n s f e r r e d w i t h the p a r t i c l e s during e v a p o r a t i o n and condensation. f) D.O. R a y l e i g h and A.W. S o m m e r (3) c o m p a r e d in 1962 h and Q+ values of interstitial atoms in metals and c o n c l u d e d that a close i n t e r r e l a t i o n should exist b e t w e e n these quantities. Since then the n u m b e r of data a v a i l a b l e has i n c r e a s e d several times and the c o m p i l a t i o n of Q+ and h in Table I shows no longer any correlation. V a l u e s of h w e r e taken from Ref. 17 and of Q+ from Ref. 4 or f r o m papers "recently published. N u m b e r s in p a r e n t h e s e s give ent h a l p i e s of f o r m a t i o n of the c o r r e s p o n d i n g m e t a l / n o n - m e t a l c o m p o u n d s w h i c h are u s u a l l y only a few kJ d i f f e r e n t from h. T h e s e c o n s i d e r a t i o n s and further a r g u m e n t s of a m o r e d e t a i l e d d i s c u s s i o n (25) show that Q+ is o b v i o u s l y that c o m p o n e n t of the total energy flux w h i c h is t r a n s f e r r e d w i t h m i g r a t i n g p a r t i c l e s in excess to the energy, h, in thermal equilibrium. The heat of solution, h, or part of it are not a priori a component of Q+. This is a c l e a r - c u t d e f i n i t i o n for the d e v e l o p m e n t of a t o m i s t i c models. References I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
Th. Hehenkamp, T h i n Solid Films 25 (1975) 281 Th. H e h e n k a m p and B. Junkermann, Z. Metallkde. 67 (1976) 103 D.O. R a l e i g h and A.W. Sommer, J. Chem. Phys. 36 (1962) 381 H. Wever, E l e k t r o - und T h e r m o t r a n s p o r t in Metallen, J.A. Barth, L e i p z i g 1973 S.R. De Groot and P. Mazur, Non E q u i l i b r i u m T h e r m o d y n a m i c s , N o r t h - H o l l a n d , A m s t e r d a m 1962 K. Wirtz, P h y s i k Z. 44 (1943) 221 A.D. Le Claire, Phys. Rev. 93 (1954) 344 J.A. Brinkmann, Phys. Rev. 93 (1954) 345 L.A. Girifalco, Phys. Rev. 128 (1962) 2630 A.R. A l n a t t and S.A. Rice, J. Chem. Phys. 33 (1960) 57 H.B. Huntington, J. Phys. Chem. Solids 29, 1641 (1968) G. Schottky, Phys. Stat. Sol. 8 (1965) 357 V.B. Fiks, Sov. Phys. S o l i d St. 5 (1964) 2549 M.J. Gerl, J. Phys. Chem. Solids 28 (1967) 725 R.A. Oriani, J. Phys. Chem. Sol. 30 (1969) 339 H. R i c k e r t and C. Wagner, Ber. Bunsenges, Physik. Chem. 67 (1963) 621
654
HEAT OF T R A N S P O R T
AND HEAT OF S O L U T I O N
Vol.
13, No.
17. E. Fromm, E. Gebhardt, eds., Gase und K o h l e n s t o f f in Metallen, S p r i n g e r B e r l i n 1976 18. S. Goto, R. Kirchheim, J. Mathuni, and E. Fromm, J. Less C o m m o n M e t a l s 59 (1978) 165 19. S. Motozumi, S. Goto, and T. Yosbida, S c r i p t a Met. 10 (1976) 357 20. J. Mathuni, O.N. Carlson, E. Fromm, and R. Kirchheim, Met. Trans. 7a (1976) 323 21. G. H6fer, Z. Naturf. 26a (1971) 1885 22. R. K i r c h h e i m and E. Fromm, A c t a Met. 22 (1974) 1543 23. H. Wipf and G. Alefeld, Phys. Stat. Sol. (a) 23 (1974) 175 24. O.D. G o n s a l e z and R.A. Oriani, Trans. AIME 233 (1965) 1878 25. J. Mathuni, Dr.-Thesis, U n i v e r s i t ~ t S t u t t g a r t 1977
TABLE Heat of T r a n s p o r t
solvent ~-Ti S-Ti ~-Zr S-Zr
~-Hf V
Ta Nb
~-Fe
~-Fe Co Ni Pd
and Heat of S o l u t i o n
solute H H C H H N 0 O H C N O N O H,D N O H,D C N C C H,D C H C
I
of I n t e r s t i t i a l s
Q+(kJ/mol)
ref
+18.5, +33.2 -2.6 -4.2 +24 +25 to +50 +105 to +126 +89 +I 26 +8.4 -20.5, -14.6 +16.7 to +29.3 +8.4 to +29.3 -29.3 t o - 4 . 2 -79.5 to -8.4 +8.4 to +12.6 O -67 to -4.2 -34.5 to -23 -I00.4, -58.6 -75.3 -8.4 to -4.2 +6.3 -6.3 to -0.84 -6.7 +6.3 +35. I
4 4 4 4 4 4 4 18 19 19 20 20 21 22 23 22 22 24 4 4 4 4 24 4 4 4
in T r a n s i t i o n
Metals
h(kJ/mol) - 46 - 59 -I 46 - 59 - 63 (-368) (-535) -552 -32.2 (- 46, -146.4) -284 -423 -182 -385 - 39.7 -178 -385 + 24.3 +106 + 34.7 + 44 + 79.5 + 16.7 + 50.2 - 10.5 + 24.3
7
Vol. 13, pp. 631-634, 1979 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved.
HEAT OF T R A N S P O R T AND HEAT OF SOLUTION
J. Mathuni,
R. Kirchheim,
and E. Fromm
M a x - P l a n c k - I n s t i t u t ffir M e t a l l f o r s c h u n g Institut ffir W e r k s t o f f w i s s e n s c h a f t e n Stuttgart, Germany (Received May 2, 1979)
Introduction In the i n t e r p r e t a t i o n of the heat of transport, Q+, obtained from steady state c o n c e n t r a t i o n profiles, the partial molal enthalpy, h, or heat of solution of the m i g r a t i n g particles has sometimes been considered to be one part of this q u a n t i t y (I-3). This point is of particular interest for the transport of interstitial atoms d i s s o l v e d in metals, e.g. H,C,N or O, since their partial molal enthalpy values, h, are r e l a t i v e l y large and frequently much higher than the heat of transport. In the O- and N-systems of V, Nb or Ta this difference exceeds in some cases one order of m a g n i t u d e (1,3,4). Thus the experimental heat of transport value should contain, in addition to h, other contributions with opposite signs but of similar magnitude, e.g. 400 kJ/mol or more. This rather u n r e a s o n a b l e consequence as well as the fact that h depends on the definition of the standard state are plausible arguments against this kind of subdivision of Q+ into components. In this paper the basic equations of entropy p r o d u c t i o n and the flux equations are analysed again under this aspect and it is d e m o n s t r a t e d by appropriate definitions and transformations, that neither h itself nor its temperature dependence are a priori contained in components of Q+ d e t e r m i n e d in an experiment. Basic Equations For one sort of mobile particles i the entropy production in a volume element that is passed by the energy flux Ju and the particle flux Ji is given by (5) (I)
~=
Ju~I/T - Ji?~T .
W i t h ) / = h - Ts = h - Ts O - TR in (~'c), c mole fraction of i and ~ a c t i v i t y effidient this equation can be t r a n s f o r m e d to
(2)
~=
Ju" V l / T
(3)
= Ju" ~ I / T
- Ji
- Ji
or with
T %ln c T
-1--
1 9 h
(4)
~ I/T c
T ~I/T
= _ _ 9S
= - CpT
~I/T
+ R
and
1+ ~ l n ~ ? I n ~in c
m =91n
91/T
631 0036-9748/79/070631-04502.00/0 Copyright (c) 1979 Pergamon Press Ltd.
91n
~ I c T
c
co-
632
HEAT OF TRANSPORT AND HEAT 0F SOLUTION
(5)
~=
Vol.
13, No. 7
(Ju-Ji'h) ~ I/T - Ji-R. (1+m) V in c
Eq. (5) and the subsequent considerations are simplified by the introduction of the following definition for the energy flux: (6)
Ju = Jq + Ji h + Ji Q+
is the heat flux due to thermal conductivity in a temperature gradient and ~ shall contain no components coupled with the particle flux J~. The energy transferred together with the particles i under the condition o~ thermal equilibrium with their surrounding is Ji-h and Q+ is the energy transferred with the particles in excess of this equilibrium value as a consequence of the specific transport mechanism present. With Eq. (5) and (6) one obtains (7)
~=
Jq V I / T
If V I/T and the expression equations are
(8) (9)
Ji = L11 {Q+~I/T
+ Ji { Q + V I / T
- R(1+m) ~ in c ~
in brackets are choosen as driving
- R(1+m)Vlncl+
Jq = L21 {Q+~I/T
L12 ~ I / T
- R(1+m)~incj
= L11 ~Q+~I/T
+ L22~1/T
forces the flux
- R(1+m)~ I n c }
= L22~1/T
From the definition of Ja in Eq. (6) and Onsagers theorem it follows that the phenomenological coefficfents L21 and L12 are zero for this specific choice of fluxes and forces. The condition Ji = O for steady state yields immediately the well known expression (10)
Q+
R(1+m) =
dln c d I/T
and for ideal systems with m = O (11)
Q+
R d in c =
I/-----T d
Thus, the physical significance of the reduced heat of transport, in steady state experiments is exactly the same as in Eq. (6). In the standard treatment with (Ju-h.J i) as transformed energy flux, nomenological coefficients L11 and L22 no longer play any role in tion of Q+ and it is not necessary to distinguish between the two transport, Q~, and reduced heat of transport, Q+ = Q~-h.
Q+, measured contrast to the two phethe definiterms heat of
In steady s t a t e , b e c o m e s a minimum and in Eq. (7) the expression in brackets is zero. Q+- Vl/T represents the entropy change due to the fact that Q+ enters and leaves a volume element together with the particles at interfaces with different temperature and R(l+m) V l n c is the entropy change due to differences in the entropy of position. In steady state both components cancel and if a particle flux Ji would pass a volume element under these conditions it could not contribute to the entropy production. Conclusions Further definitions
and conclusions
derived from the equations used are:
Vol.
13, No.
7
HEAT OF T R A N S P O R T AND HEAT OF SOLUTION
633
a) The e x p r e s s i o n (Ju-Jih) in Eq. (5) states that the heat of s o l u t i o n transferred t o g e t h e r w i t h the i atoms is a c o m p o n e n t of the total e n e r g y flux Ju w h i c h does not change the e n t r o p y p r o d u c t i o n ~ . O n l y that part of the energy w h i c h is t r a n s f e r r e d w i t h m i g r a t i n g p a r t i c l e s in excess to the e q u i l i b r i u m energy h at the t e m p e r a t u r e c o n s i d e r e d can affect the e n t r o p y production. This d i f f e r e n c e in the energy flux term a u t o m a t i c a l l y solves the p r o b l e m of the a r b i t r a r y d e f i n i t i o n of the s t a n d a r d state of h and c o n s e q u e n t l y also of the total energy flux Ju" b) The t e m p e r a t u r e d e p e n d e n c e of h and s cancel in Eq. (3) and thus they are not able to i n f l u e n c e Q+. c) The a t o m i s t i c m o d e l s p r e s e n t l y d i s c u s s e d are c o n s i s t e n t w i t h the interpret a t i o n of Q+ used in Eq. (6). In W i r t z - t y p e models (6-10) Q+ is the activation energy or part of it. A jumping atoms gathers this energy from its surr o u n d i n g in the starting p o s i t i o n and releases it again to the lattice as heat e n e r g y after the jump. In e l e c t r o n drag theories (11-14) it is the difference in the energy t r a n s f e r b e t w e e n jumping p a r t i c l e s in the saddle point and e l e c t r o n and/or hole currents flowing p a r a l l e l and antiparallel, respectively, to the t e m p e r a t u r e gradient. ~+ (Ju-Jih) ; . d) The d e f i n i t i o n U = ~ ~T an~ further c o n c l u s i o n s d e r i v e d from this e x p r e s s i o n by Oriani (15) are in a g r e e m e n t w i t h the present i n t e r p r e t a t i o n of Q+. e) If t r a n s p o r t p h e n o m e n a are d i s c u s s e d in systems w h e r e the e x c h a n g e of particles w i t h the s u r r o u n d i n g gas a t m o s p h e r e occurs, the heat of solution, h, has to be c o n s i d e r e d in the t h e o r e t i c a l treatment, as it has been done, e.g., by H. Rickert and C. W a g n e r (16) because this energy is really t r a n s f e r r e d w i t h the p a r t i c l e s during e v a p o r a t i o n and condensation. f) D.O. R a y l e i g h and A.W. S o m m e r (3) c o m p a r e d in 1962 h and Q+ values of interstitial atoms in metals and c o n c l u d e d that a close i n t e r r e l a t i o n should exist b e t w e e n these quantities. Since then the n u m b e r of data a v a i l a b l e has i n c r e a s e d several times and the c o m p i l a t i o n of Q+ and h in Table I shows no longer any correlation. V a l u e s of h w e r e taken from Ref. 17 and of Q+ from Ref. 4 or f r o m papers "recently published. N u m b e r s in p a r e n t h e s e s give ent h a l p i e s of f o r m a t i o n of the c o r r e s p o n d i n g m e t a l / n o n - m e t a l c o m p o u n d s w h i c h are u s u a l l y only a few kJ d i f f e r e n t from h. T h e s e c o n s i d e r a t i o n s and further a r g u m e n t s of a m o r e d e t a i l e d d i s c u s s i o n (25) show that Q+ is o b v i o u s l y that c o m p o n e n t of the total energy flux w h i c h is t r a n s f e r r e d w i t h m i g r a t i n g p a r t i c l e s in excess to the energy, h, in thermal equilibrium. The heat of solution, h, or part of it are not a priori a component of Q+. This is a c l e a r - c u t d e f i n i t i o n for the d e v e l o p m e n t of a t o m i s t i c models. References I. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
Th. Hehenkamp, T h i n Solid Films 25 (1975) 281 Th. H e h e n k a m p and B. Junkermann, Z. Metallkde. 67 (1976) 103 D.O. R a l e i g h and A.W. Sommer, J. Chem. Phys. 36 (1962) 381 H. Wever, E l e k t r o - und T h e r m o t r a n s p o r t in Metallen, J.A. Barth, L e i p z i g 1973 S.R. De Groot and P. Mazur, Non E q u i l i b r i u m T h e r m o d y n a m i c s , N o r t h - H o l l a n d , A m s t e r d a m 1962 K. Wirtz, P h y s i k Z. 44 (1943) 221 A.D. Le Claire, Phys. Rev. 93 (1954) 344 J.A. Brinkmann, Phys. Rev. 93 (1954) 345 L.A. Girifalco, Phys. Rev. 128 (1962) 2630 A.R. A l n a t t and S.A. Rice, J. Chem. Phys. 33 (1960) 57 H.B. Huntington, J. Phys. Chem. Solids 29, 1641 (1968) G. Schottky, Phys. Stat. Sol. 8 (1965) 357 V.B. Fiks, Sov. Phys. S o l i d St. 5 (1964) 2549 M.J. Gerl, J. Phys. Chem. Solids 28 (1967) 725 R.A. Oriani, J. Phys. Chem. Sol. 30 (1969) 339 H. R i c k e r t and C. Wagner, Ber. Bunsenges, Physik. Chem. 67 (1963) 621
654
HEAT OF T R A N S P O R T
AND HEAT OF S O L U T I O N
Vol.
13, No.
17. E. Fromm, E. Gebhardt, eds., Gase und K o h l e n s t o f f in Metallen, S p r i n g e r B e r l i n 1976 18. S. Goto, R. Kirchheim, J. Mathuni, and E. Fromm, J. Less C o m m o n M e t a l s 59 (1978) 165 19. S. Motozumi, S. Goto, and T. Yosbida, S c r i p t a Met. 10 (1976) 357 20. J. Mathuni, O.N. Carlson, E. Fromm, and R. Kirchheim, Met. Trans. 7a (1976) 323 21. G. H6fer, Z. Naturf. 26a (1971) 1885 22. R. K i r c h h e i m and E. Fromm, A c t a Met. 22 (1974) 1543 23. H. Wipf and G. Alefeld, Phys. Stat. Sol. (a) 23 (1974) 175 24. O.D. G o n s a l e z and R.A. Oriani, Trans. AIME 233 (1965) 1878 25. J. Mathuni, Dr.-Thesis, U n i v e r s i t ~ t S t u t t g a r t 1977
TABLE Heat of T r a n s p o r t
solvent ~-Ti S-Ti ~-Zr S-Zr
~-Hf V
Ta Nb
~-Fe
~-Fe Co Ni Pd
and Heat of S o l u t i o n
solute H H C H H N 0 O H C N O N O H,D N O H,D C N C C H,D C H C
I
of I n t e r s t i t i a l s
Q+(kJ/mol)
ref
+18.5, +33.2 -2.6 -4.2 +24 +25 to +50 +105 to +126 +89 +I 26 +8.4 -20.5, -14.6 +16.7 to +29.3 +8.4 to +29.3 -29.3 t o - 4 . 2 -79.5 to -8.4 +8.4 to +12.6 O -67 to -4.2 -34.5 to -23 -I00.4, -58.6 -75.3 -8.4 to -4.2 +6.3 -6.3 to -0.84 -6.7 +6.3 +35. I
4 4 4 4 4 4 4 18 19 19 20 20 21 22 23 22 22 24 4 4 4 4 24 4 4 4
in T r a n s i t i o n
Metals
h(kJ/mol) - 46 - 59 -I 46 - 59 - 63 (-368) (-535) -552 -32.2 (- 46, -146.4) -284 -423 -182 -385 - 39.7 -178 -385 + 24.3 +106 + 34.7 + 44 + 79.5 + 16.7 + 50.2 - 10.5 + 24.3
7